Ferroelectric ultrathin perovskite films

ABSTRACT

Disclosed herein are perovskite ferroelectric thin-film. Also disclosed are methods of controlling the properties of ferroelectric thin films. These films can be used in a variety materials and devices, such as catalysts and storage media, respectively.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the National Stage of International Application No.PCT/US2007/086316, filed Dec. 3, 2007, which claims the benefit of U.S.Provisional Application No. 60/872,273, filed Dec. 1, 2006, thedisclosures of which are incorporated herein by reference in theirentireties.

STATEMENT OF GOVERNMENT INTERESTS

The invention was made with U.S. Government support. The Government mayhave certain rights in the invention under U.S. Department of Energy,Office of Science, Basic Energy Sciences under Contract No.W-31-109-ENG-38, NSF DMR-0313764, ECS-0210449, ONR N00014-00-1-0372,N00014-01-1-0365 and AFOSR FA9550-04-1-0077.

FIELD OF THE INVENTION

The disclosed invention pertains to the field of ferroelectric films.The disclosed invention also pertains to perovskite compositions. Thedisclosed invention is also in the field of switchable perovskite films.The disclosed invention also pertains to the field of storage media andcatalysis.

BACKGROUND OF THE INVENTION

One of the outstanding fundamental needs for ferroelectric thin films isdeveloping a stable polar phase when the polarization has a componentperpendicular to the film plane. Although such orientations are desiredfor many applications and can be obtained (e.g., by compressiveepitaxial strain), the polarization change at the film boundariescreates a “depolarizing field” that should be neutralized for the polarphase to be stable. Two mechanisms appear to be available to reduce thedepolarizing field energy: compensation by free charge at the boundariesor the formation of equilibrium stripe domains with oppositely orientedpolarization. In both cases, the trade-off between bulk energy gain andsurface energy cost leads to a suppression of the phase transition tothe polar phase as films become thinner. These fundamental size effectsmay dramatically alter behavior in ultrathin films.

SUMMARY OF THE INVENTION

Accordingly, one aspect of the present invention provides methods ofreversibly switching the polarization of a ferroelectric film bychanging the chemical environment in contact with one surface of aferroelectric film. In these methods, the chemical environment can bechanged by controlling the oxygen partial pressure in contact with theferroelectric film. For example, the change in oxygen partial pressureinduces an outward or inward polarization, respectively, in theferroelectric film. In other embodiments, the ferroelectric filmcomprises a perovskite thin-film. Suitable perovskite thin-filmscomprises PbTiO₃. In the other types of perovskite and films can also beutilized. Suitably, the ferroelectric film is supported on a conductingsubstrate. In particularly preferred embodiments, the ferroelectricfilms are thinner than 10 nm, and typically at least about 1 nm.

Another aspect of the present invention provides ferroelectric thin-filmcomprising a perovskite film thinner than 10 nm supported on aconducting substrate, the perovskite film comprising polar ground statesin the presence of ionic adsorbates. Suitable perovskite thin-filmscomprise PbTiO₃. In other embodiments, the conducting substrates cancomprise strontium ruthenium oxide or strontium titanium oxide. Asuitable film thickness is greater than or about 1.2 nm. In certainpreferred embodiments, the conducting substrate comprises an epitaxialconducting film. These ferroelectric thin films have uses in switchablecatalysts and storage media.

The present invention also provides methods of inverting a domain in aferroelectric thin-film, comprising applying a voltage to a probe tipadjacent to the ferroelectric thin-film. For example, in these methodsthe ferroelectric thin-film can comprise a perovskite film thinner than10 nm supported on a conducting substrate, the perovskite filmcomprising polar ground states in the presence of ionic adsorbates.Suitable perovskite thin-films comprise PbTiO₃. In other embodiments,the conducting substrates can comprise strontium ruthenium oxide orstrontium titanium oxide. A suitable film thickness is greater than orabout 1.2 nm. In certain preferred embodiments, the conducting substratecomprises an epitaxial conducting film.

Another aspect of the present invention provides methods of writing adata bit in a ferroelectric thin-film, comprising: applying a voltage toa probe tip adjacent to the ferroelectric thin-film. For example, inthese methods the ferroelectric thin-film can comprise a perovskitethin-film thinner than 10 nm supported on a conducting substrate, theperovskite film comprising polar ground states in the presence of ionicadsorbates. Suitable perovskite thin-films comprise PbTiO₃. In otherembodiments, the conducting substrates can comprise strontium rutheniumoxide or strontium titanium oxide. A suitable film thickness is greaterthan or about 1.2 nm. In certain preferred embodiments, the conductingsubstrate comprises an epitaxial conducting film.

In another aspect, the present invention also provides methods forreducing the Curie temperature of a ferroelectric thin-film, comprising:reducing the thickness of the ferroelectric thin-film to less than 10nm.

In yet other aspects, the present invention also provides methods ofstabilizing the polar state in a thin-film, comprising: absorbing ionsonto the thin-film surface. For example, in these methods the surfacecharge is passivated by adsorbing an adsorbate. Suitable thin-filmscomprise a ferroelectric material characterized as having a mono-domainstate.

The present invention also includes aspects which include methods forelectrically switching the reactivity of a ferroelectric thin-filmsurface, comprising: applying a voltage adjacent to the ferroelectricthin-film. A suitable ferroelectric thin-film comprises a perovskitefilm thinner than 10 nm supported on a conducting substrate. Forexample, the perovskite film may comprise polar ground states in thepresence of ionic adsorbates.

Using in situ high-resolution synchrotron x-ray scattering, the Curietemperature T_(C) has been determined for ultrathin c-axis epitaxialPbTiO3 films on conducting substrates (SrRuO3 on SrTiO3), with surfacesexposed to a controlled vapor environment. The suppression of TC wasrelatively small, even for the thinnest film (1.2 nm). We observe that180° stripe domains do not form, indicating that the depolarizing fieldis compensated by free charge at both interfaces. This is confirmed byab initio calculations that find polar ground states in the presence ofionic adsorbates.

Here we focus on stabilization of the single-domain state in ultrathinferroelectric perovskite films by interfacial charge. Key issues aredetermining the critical thickness, below which the monodomain,perpendicularly polarized state is not stable, and understanding thenature of the interfacial charge compensation. Previous experimentalstudies of ultrathin epitaxial films on conductive substrates have beencarried out using electrical measurements, piezoresponse forcemicroscopy (PFM), and x-ray lattice parameter measurements. Thesestudies have found stable monodomain ferroelectricity at roomtemperature in films as thin as 3-4 nm. Lattice parameter measurementsindicated a 50% reduction in PbTiO3 polarization when film thickness wasreduced to 3 nm, which was explained using a model based on the finitescreening length for charge in conducting electrodes. Interestingly, insome of these studies, the film did not have an electrode on the exposedsurface. Interface compensation adequate to stabilize ultrathin polarfilms can occur by a mechanism other than electronic conduction, e.g.,by the accumulation of charged ions. For relatively thick ferroelectricfilms exposed to ambient atmosphere, there is strong experimentalevidence for surface compensation by ionic adsorption. Furthermore,monodomain ferroelectric films have been observed on nonconductingsubstrates, and it has been proposed that high-mobility electrons canexist at heterointerfaces in perovskite insulators due to unusualbonding states. The adequacy of these alternative, “chemical” ratherthan “electronic” mechanisms for reducing depolarization field energysufficiently to stabilize ultrathin polar films is relativelyunexplored.

Using real-time x-ray scattering, we also observe that the direction ofpolarization in a ferroelectric thin film can be reversibly switched bychanging the oxygen partial pressure in equilibrium with its surface.

The reorientable spontaneous electric polarization of ferroelectricmaterials gives them unusual dielectric properties and utility forinformation storage. Polarization orientation is typically switched byapplying a voltage across electrodes. Here we report real-timesynchrotron x-ray scattering experiments showing that the polarizationcan also be reversibly switched by changing the chemical environment incontact with one surface of a ferroelectric film. High or low oxygenpartial pressure induces outward or inward polarization, respectively,in a PbTiO3 film. Such chemical switching provides a new mechanism formanipulation of ferroelectric domain patterns and for novel applicationssuch as chemical actuators and active catalysts.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1. Shows X-ray scattering intensity along the 30 L CTR, showing the304 Bragg peaks and finite-thickness fringes from 9.2-nm thick PbTiO3and 50-nm-thick SrRuO3 films at various temperatures. The shift of thePbTiO3 peak to lower q_(z) upon cooling indicates an expansion of the clattice parameter.

FIG. 2. Shows the c lattice parameter vs T for each film, with solidlines showing the break in slope used to estimate T_(C). The upper curveis the Landau theory prediction for thick PbTiO3 on SrTiO₃.

FIG. 3. Shows PbTiO3 T_(C) vs film thickness for monodomain films onconducting SrRuO3 (this work) and stripe-domain films on insulatingSrTiO3 (previous work, D. D. Fong, et al., Science 304, 1650 (2004)).Curves are guides to the eye.

FIG. 4. Shows bistability of lattice parameter, domain fraction, and netpolarization as a function of oxygen partial pressure pO₂ for a 10 nmthick PbTiO₃ film on SrRuO₃/SrTiO₃. Blue and red curves are fortemperatures of 645 K and 735 K, respectively. Circles anddownward-pointing triangles are obtained when decreasing from high pO₂;squares and upward-pointing triangles when increasing from low pO₂. Tofully switch the sample to negative polarization, oxygen flow was set tozero, resulting in an indeterminate low value of pO₂ indicated by linesleading off scale on left. (A) Measured c lattice parameter, showingchemical butterfly loops. (B) Positive domain fraction and (C) netpolarization obtained from fits of L scans to a detailed structuralmodel. (D) Illustration of chemical switching of polarization, showingfully polarized extreme states I and III. Circled and uncircled symbolsrepresent the bound charges of the ferroelectric and the freecompensating charges, respectively.

FIG. 5. Shows X-ray scattering patterns along the L direction throughthe PbTiO₃, SrRuO₃, and SrTiO₃ 304 peaks from films equilibrated underoxidizing (pO₂=3.1 mbar) and reducing (pO₂=3.3×10⁻⁶ mbar) ambients at645 K. Black curve: before FIG. 6 switch, oxidizing condition. Bluecurve: after switching to reducing condition. Red points: after FIG. 3switch, oxidizing condition. Values of L are given in reciprocal latticeunits of the SrTiO₃ substrate at 298 K, which has a cubic latticeparameter of 3.9051 Å.

FIG. 6. Shows time evolution of x-ray scattering distribution near thePbTiO₃ 304 peak during switching from oxidizing (pO₂=3.1 mbar) toreducing (pO₂=3.3×10⁻⁶ mbar) conditions and back. (A) Distribution alongthe L (out-of-plane) direction at H=2.989, K=0.13 (B) Distribution alongthe K (in-plane) direction at H=2.989, L=3.810. Redder hues indicatehigher intensity (log scale).

FIG. 7. Shows time dependence of quantities extracted from x-rayscattering measurements during chemical switching cycle shown in FIG. 6.(A) Lattice parameter c. (B) Positive domain fraction.

FIG. 8. Fit of model for positively polarized monodomain structure (blueline) to data (red circles) for pO₂=3.0 mbar, T=645 K. Peaks (from leftto right) are 304 Bragg peaks of PbTiO₃, SrRuO₃, and SrTiO₃.

FIG. 9. Calculated intensity at PbTiO₃ 304 peak position as a functionof positive domain fraction x_(pos) for three values of incoherentfraction f_(inc).

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Described herein is the paraelectric-ferroelectric phase transition inultrathin PbTiO3 films grown on conducting substrates, with surfacesexposed to a controlled vapor environment. The structures of films asthin as 1.2 nm (3 unit cells) were determined as a function oftemperature (T) using high-resolution grazing-incidence x-rayscattering. The polar phase was observed to form and remain singledomain for all thicknesses studied (1.2-9.2 nm). The observed stabilityof the monodomain phase is explained by ab initio calculations that finda polar ground state if ionic adsorbates are present on the surface. Thepolarization direction depends on the chemical nature of the adsorbate.

The conducting substrates were epitaxial SrRuO3 films grown onSrTiO₃(001) single crystals by pulsed laser deposition. The PbTiO3 filmswere grown by metalorganic chemical vapor deposition (MOCVD) underconditions described previously. Grazing-incidence synchrotron x-rayscattering was used for in situ monitoring of the film during epitaxialgrowth and for subsequent observation of the phase transition as afunction of T. This method allows study at high T while maintaining filmstoichiometry and a well-controlled vapor interface and the study offerroelectricity in films too thin to be characterized by other methods.Four PbTiO3 films of different thickness were studied: Three of thefilms (1.2, 2.0, and 3.6 nm) were grown at 930 K on 10-nm-thick SrRuO3layers; the thickest PbTiO3 film (9.2 nm) was grown at 990 K on a50-nm-thick SrRuO3 layer. All of the layers replicated the highcrystalline quality of the substrates (0.01° typical mosaic) and weremeasured to be fully lattice matched to the underlying SrTiO3. Thiscompressive epitaxial strain produces polarization perpendicular to thefilm plane.

X-ray experiments were carried out at beam line 12ID-D of the AdvancedPhoton Source, as described previously in S. K. Streiffer, et al., Phys.Rev. Lett. 89, 067601 (2002). The Curie temperature TC was determined bymeasuring the T dependence of the c (out-of-plane) lattice parameter.FIG. 1 shows measurements along the 30 L crystal truncation rod (CTR)for a 9.2 nm- (23 unit-cell-) thick PbTiO3 film at various temperatures.This region of the CTR extends through the 304 peaks of PbTiO3, SrRuO3,and SrTiO3. From the position of the PbTiO3 peak, one can see that cincreases as the film polarizes below TC, because of the strongpolarization-strain coupling in this system [2]. The many fringesobserved from the thicknesses of the SrRuO3 and PbTiO3 layers indicatethe high quality of the interfaces.

For the 9.2 nm film, we also performed ex situ room-T PFM. We were ableto “write” inverted domains by applying a positive voltage to the tipand to determine that the as grown state of the film was a single domainhaving a polarization directed out of the film (“up” polarization). Forall films, we searched in situ near TC for satellites in the diffusex-ray scattering around the PbTiO3 Bragg peaks, which occur whenequilibrium 180° stripe domains are present. None were observed,indicating that all the films transform directly into the monodomainpolar state.

Values for the PbTiO3 lattice parameter c as a function of T weredetermined by fitting the x-ray CTR data to a 3-layer model (two filmsand a substrate). For the fits shown here, we assumed that the PbTiO3polarization direction is up, with the square of atom displacementsproportional to the change in c from its P=0 value, and that the SrRuO3is SrO terminated and the PbTiO3 is PbO terminated. Changing theseassumptions does not significantly affect the results for c. For eachsample, the numbers of PbTiO3 and SrRuO3 unit cells were fixed. Eightparameters were varied in the fitting procedure: lattice constants,layer roughnesses, and interface offsets for the SrRuO3 and PbTiO3layers, a scale factor for the SrRuO3, and an overall scale factor forthe total scattered intensity. This simple structural model is able toreproduce the CTR intensities very well for all thicknesses andtemperatures. Typical best fits are shown with the data in FIG. 1.

FIG. 2 shows the dependence of c on T for each film thickness, as wellas the predicted T dependence of c for thick, coherently strained PbTiO3lattice-matched to SrTiO3. In the thick limit, the (second order)nonpolar to polar transition is located at T_(C) ^(∞)=1025 K, asindicated by the abrupt change in slope. We extracted T_(C) for eachfilm by estimating the temperature at which the slope of c(T) changed,as shown by the solid lines in FIG. 2. The theoretical slope was usedabove T_(C). Since we have no data above T_(C) for the 3.6 nm film, thatestimate of T_(C) is a lower bound.

These results stand in some contrast to recently reported room-T latticeparameters of PbTiO3 films on Nb-doped SrTiO3 substrates, which showed adecrease in c for thinner films. We see no change in c as a function ofthickness at our lowest T (550 K), even for smaller thicknesses thanpreviously measured, although there is a clear variation in T_(C) withthickness. Note also that we observe a systematic change in c withthickness in the nonpolar phase. Caution should thus be used whenrelating c to polarization or T_(C) suppression in ultrathin films usingmeasurements at only one T.

The values of T_(C) as a function of film thickness are shown in FIG. 3.Also shown are values of T_(C) for PbTiO3 grown directly on insulatingSrTiO3, in which 180° stripe domains have formed. In both cases, T_(C)increases towards the calculated T_(C) ^(∞) for thick films anddecreases by hundreds of degrees below this limit for ultrathin films.The transition temperatures for PbTiO3 on SrRuO3 are somewhat higherthan those on SrTiO3, in agreement with the observed difference in theequilibrium domain morphology: The conducting SrRuO3 electrode lowersthe energy of the single-domain state, producing a direct transitionfrom unpolarized to monodomain polarized at a higher T_(C). Thedependence of T_(C) ^(∞)-T_(C) on film thickness we observe does notobey the power law predicted by the simplest theories of screening inelectrodes but, instead, appears to be similar to that previously seenfor films on insulating substrates.

The observation that polarization occurs without formation of 180°domains implies that both the top and bottom interfaces of these filmsshould be almost completely compensated by free charge. Thus, a SrRuO3electrode will compensate PbTiO3 with a voltage offset small enough thateven a 3-unit-cell-thick film polarizes above room temperature. This isin agreement with recent ab initio calculations on films with two SrRuO3electrodes. The behavior of the top surface is perhaps even moreintriguing—although there is no conductor to supply electronic charge,exposure to the ambient vapor of the MOCVD growth environment evidentlysupplies sufficient free charge from ions to neutralize the depolarizingfield.

To quantitatively verify whether adsorbed ions can stabilize the polarstate in ultrathin films, we have performed ab initio density functionaltheory (DFT) calculations on the structure and energetics of PbTiO3films on SrRuO3 bottom electrodes with various molecules adsorbed to thesurface. Based on the composition of the MOCVD environment, we chose tostudy H, O, OH, H₂O, and CO₂ adsorption. Calculations were performedusing methods described previously in Na Sai, A. M. Kolpak, and A. M.Rappe, Phys. Rev. B 72, 020101(R) (2005). We used DFT with thegeneralized gradient approximation as implemented in the ab initio codeDACAPO, with ultrasoft pseudopotentials generated with the VASP code, aplane wave cutoff of 400 eV, a 4×4×1 Monkhorst-Pack k-point mesh, and anfast-Fourier-transform grid of 8 points/{acute over (Å)} in all 3directions. We modeled 3-unit-cell- (1.2-nm-) thick PbTiO3 filmssupported by 3 unit cells of SrRuO3, with a SrO—TiO2 interface betweenPbTiO3 and SrRuO3 and a PbO terminated PbTiO3 surface. A vacuum of >2 nmseparated periodic copies of the structures in the directionperpendicular to the surface, and a dipole correction was included inthe center of the vacuum region to remove the artificial electric fielddue to the asymmetry in “electrode” materials. The in-plane latticeconstant was fixed to the calculated zero-stress a value for bulkPbTiO3, which approximates the effect of the SrTiO3 substrate in theexperiments. Data are reported for films with one adsorbate on a singleunit-cell surface area; modeling of the c(2×2) surface showed that theexperimentally and theoretically determined reconstruction was presentboth with and without adsorbates but did not significantly affect theenergy difference between the bare and adsorbed states.

For a bare surface, the ground state of the ferroelectric film was foundto be nonpolar. With OH, O, or H adsorbates present, however, the groundstate was polar, with atoms displaced from the centrosymmetricpositions. Table I gives values of polarization relative to thetheoretical bulk value P_(bulk)=0.75 Cm², calculated from the averageover all PbO and TiO2 layers of the cation-anion displacementsΔz=z_(cation)−z_(O), each divided by the corresponding Δz in bulktheoretical PbTiO3. Since the conductive SrRuO3 electrode can provideeither positive or negative compensation charge, the chemical nature ofthe adsorbate determines the direction of polarization. An overlayer ofOH or O, which bind to the surface Pb, enforces an upwards polarization,while an overlayer of H, which bind to the surface O, stabilizespolarization in the opposite direction. On the other hand, CO₂adsorption gives a very weak polarization, and undissociated H2Omolecules bind only weakly to the surface, preserving the nonpolarstate.

Table I also shows the differences in energy ΔE_(DFT) between the filmwith bound adsorbate and the separated bare film and free adsorbate atom(or OH molecule). To compare these T=0 K energies to experimentalconditions, we estimated the standard Gibbs free energy of adsorptionΔG⁰(T)=ΔH⁰(T)−TΔS⁰(T). The change in enthalpy ΔH° is estimated fromΔE_(DFT) by adding PΔV ≅−k_(B)T. A small correction for zero-pointenergy and spin polarization is also applied for the case of OHadsorption.

TABLE 1 Polarization and ΔE_(DFT) from DFT calculations, with estimatedreaction energies per adsorbate at T = 300 K. ΔE_(DFT) ΔH⁰ ΔG⁰ ΔGAdsorbate P/|P_(bulk)| (eV) (eV) (eV) (eV) OH 0.7 −2.00 −2.34 −1.96−0.20 O 0.9 −0.92 −0.95 −0.52 1.95 H −0.8 −2.90 −2.93 −2.65 0.79

The change in entropy ΔS₀ is primarily due to the differences betweenthe bound and free adsorbates. We estimated the entropy of the boundadsorbates and used tabulated entropies for free OH, O, and H at 1 bar[26]. Values of ΔG° at T=300 K are given in Table I. The free energychange under experimental conditions is ΔG=Δ{tilde over(G)}^({dot over (0)})−k_(B){tilde over (T)} ln p_(exp). where p_(exp) isthe adsorbate partial pressure. For these experiments, the partialpressure of O₂ was controlled at 3.3×10⁻³ bar, while that of H₂O variedbetween 2×10⁻⁶ and 1×10⁻⁹ bar depending upon the reactions of the MOCVDprocess gases. To obtain the values of ΔG in Table I, the partialpressures of free O, H, and OH at T=300 K were calculated usingp_(H2O)=5×10⁻⁷ bar. Inspection of these ΔG values shows that only OHadsorption is thermodynamically favored in our experimental environment.

The thermodynamic stability of OH adsorbates implies that the stablemonodomain polarization direction is up, in agreement with the PFMresult. The simple thermodynamic estimate presented here suggests thatthe full coverage of OH would desorb from the 3-unit-cell-thick filmabove T=450 K, resulting in a nonpolar film. Preliminary calculationsthat allow for partial coverage of OH give a higher transition T, incloser agreement with the observed T_(C)=700 K.

The DFT results presented herein verify that surface charge passivationby OH adsorbates is indeed adequate to stabilize the observed monodomainstate in these films. For ultrathin films, the chemisorption energy of 2eV is much larger than the bulk free energy difference between the polarand nonpolar states at zero field (e.g., 0.2 eV per unit-cell area for a3-unit-cell-thick film). Such a strong influence of interfacialchemistry on polarization has broad implications for ultrathinferroelectric films. To understand polarization stability, it isnecessary for measurements to be performed with controlled interfacialchemistry. The behavior of ferroelectric films with exposed surfaces maydiffer significantly from those sandwiched between two electrodes. Inthe former case (e.g., PFM experiments), and without being bound by anytheory of operation, it is believed that the switching mechanism likelyinvolves a change in adsorbate. Charged impurities at buried interfacesmay play a similar chemical role to the surface-adsorbed ions consideredhere. Exploitation of these effects for novel devices or templatingtechniques is possible, both through chemical control of polarity andthrough polarization control of ionic adsorption.

The ability to electrically switch the polarization of a ferroelectricfilm provides the basis for devices such as non-volatile ferroelectricmemories. A direction of recent research has been to understand thebehavior of ultrathin films, for which interfacial effects begin todominate over the physics of the film interior. For example, interfacepotentials due to finite electronic screening lengths and work functionsshould be considered when attempting to understand the stability of thepolar state. These have large effects in ultrathin films because theelectric field they produce scales inversely with film thickness. Inparticular, the voltage required to induce polarization reversal inultrathin films is similar in magnitude to these interface potentials.Recent studies have shown that monodomain polarization can be stabilizedin thin films not only through the presence of electrodes that provideelectronic compensation at the film interfaces but also throughsurface-adsorbed ions or charged interfacial defects/impurities.

Compensation of ferroelectric surfaces by adsorbed ions can also beinferred from electric force microscopy measurements. This chemicalnature of the environment interacts strongly with the polarization ofthin films, since the electrochemical potential created by changes inthe ambient becomes an alternative source of voltage to control filmpolarization. In particular, previous density functional theorycalculations indicated that the electronegativity of adsorbates coulddetermine the direction of polarization. Here, we use real-timesynchrotron x-ray scattering to experimentally investigate changes inthe polarization of PbTiO₃ films induced by varying the chemistry of thevapor above the film surface.

We observe that the sign of the polarization can be reversibly switchedby changing the partial pressure of oxygen in equilibrium with the filmsurface. The dependence of film lattice parameter on oxygen partialpressure (pO₂) is bistable, following a “butterfly loop” analogous tothat observed under applied voltage. The samples consist of 10-nm-thickPbTiO₃ films grown on SrRuO₃ films on SrTiO₃ (001) substrates (20). Bothepitaxial films are coherently strained to the SrTiO₃ in-plane latticeparameter, forcing the polarization orientation in the PbTiO₃ to beperpendicular to the film plane. The conductive SrRuO₃ layer provideselectronic compensation of the bottom interface of the PbTiO₃, while thetop surface is exposed to a controlled vapor ambient. The equilibriumstructure in an oxidizing environment is a monodomain state withpositive polarization, i.e. with polarization vector pointing out of thesurface.

Chemical switching experiments were carried out with the sample attemperatures in the range 550-950 K by exposing it to various pO₂ levelsin a flowing nitrogen ambient with a constant total pressure of 13 mbar.Polarization switching was observed by using synchrotron x-rayscattering to directly monitor the atomic-scale structure of theferroelectric film. By fitting a structural model to the complexscattering pattern produced by interference between nearby film andsubstrate Bragg peaks, we can extract not only the c-axis (surfacenormal) lattice parameter but also the fraction of positive domains inthe PbTiO₃ film. The position of the PbTiO₃ Bragg peak gives the latticeparameter c, while its intensity is related to the domain fractionx_(pos). Peaks with relatively large Miller index L (e.g. L=4) areespecially sensitive to x_(pos), since at high L oppositely polarizeddomains scatter nearly out of phase, resulting in a minimum in theintensity when equal fractions of positive and negative domains arepresent (x_(pos)=0.5).

FIGS. 4A and 4B show the lattice parameter and domain fraction as afunction of pO₂ for temperatures of 645 and 735 K. FIG. 4C shows thecalculated net polarization (20). The behavior of the lattice parameterin FIG. 4A is bistable, with a pO₂ dependence that changes signdepending on whether the sample is initially equilibrated at high or lowpO₂. The behavior is analogous to the standard “butterfly loop” whichoccurs when the polarization of a ferroelectric film is switched usingan external voltage applied across electrodes. Here the external pO₂ isproducing the electric field in the film. The change from point I to IIis due to piezoelectric compression of the positively polarized film byan increasingly negative field, while the state change from point II toIII is the transition from positive to negative polarization viaformation of a mixed domain state and the growth of negatively polarizeddomains. In the second half cycle, the transition from III to IV is dueto piezoelectric compression of the negatively polarized film underincreasingly positive field; finally, from IV to I the film switchesback to positive polarization.

The results in FIGS. 4A-C indicate that the ferroelectric film can befully switched between monodomain states with positive and negativepolarization orientations by varying the pO₂ of the ambient, asillustrated in FIG. 4D. The change in sign of the lattice parameterdependence on pO₂ demonstrates that the film polarization is oppositewhen equilibrated at high or low pO₂. We observe that the bistablebehavior is repeatable, provided that the excursions in pO₂ are largeenough to fully switch the sample. For small changes in pO₂ in thenon-switching regions (x_(pos) near unity or zero), the measured strainremains on one of the two branches of the loop with no hysteresis, andequilibration is relatively rapid (within minutes). While a pO₂ of 3.0mbar is sufficient to fully switch the sample to positive polarization,full switching to negative polarization could be accomplished mostrapidly at pO₂ values below the minimum controllable value in theapparatus (3.3×10⁻⁶ mbar). For the data in FIG. 4, full switching tonegative polarization was obtained by setting the oxygen input flow tozero, giving a value of pO₂ less than 10⁻⁷ mbar. Similar behavior isobserved at both temperatures, with overall smaller c lattice parametersat the higher temperature consistent with those expected as the Curiepoint T_(C)≈920 K (10) is approached and polarization magnitudesdecrease. We observe that there is no bistability in c as a function ofpO₂ at T=950 K, in the paraelectric phase above T_(C).

Further evidence that the polarization switching is reversible (i.e.returns to an identical state) is given in FIG. 5, which showsdistributions of scattering in the L direction (L scans) through the 304Bragg peaks. The black, blue and red curves, respectively, were takenwith the sample equilibrated (i) at high pO₂ (3.0 mbar), before aswitching cycle; (ii) at low pO₂ (3.3×10⁻⁶ mbar), and (iii) again atpO₂=3.0 mbar, after the switching cycle. The three main peaks are the304 Bragg reflections from the PbTiO₃, SrRuO₃, and SrTiO₃, respectively.The PbTiO₃ and SrRuO₃ peaks are broadened and surrounded by fringesarising from the finite film thickness and film/substrate interferenceeffects. The intensity of the PbTiO₃ peak and the interference fringepattern are sensitive to the polarization structure of the film. Theintensity distribution obtained after the film is switched back to theoxidizing ambient is indistinguishable from that of the initial state,indicating that the initial polarization structure is recovered. Thewide extent of the finite-thickness oscillations under both high and lowpO₂ conditions implies that the polarization and lattice parameter areapproximately constant throughout the film thickness. Furthermore, theperiod of these oscillations indicates that the thickness of theperovskite structure PbTiO₃ is the same in both states. We do notobserve formation of second phases, as has been seen in annealing ofpowders. This is consistent with the lack of a high concentration ofextended defects in these films, which are necessary for significantmass transport in the bulk of the film at these temperatures. Toinvestigate the switching dynamics, we performed real-time reciprocalspace mapping of the x-ray scattering intensity around the PbTiO₃ 304Bragg peak during chemical switching between high and low pO₂ states.

FIG. 6A shows the intensity along the L scan as a function of timeduring switching at a temperature of 645 K. The most intense (red)feature is the PbTiO₃ Bragg peak. FIG. 7 shows the time evolution of 7the lattice parameter c and domain fraction x_(pos) obtained by fittingthese L scans. At time t=0, the pO₂ is changed from 3.0 mbar to 3.3×10⁻⁶mbar. One can see that the PbTiO₃ peak quickly shifts to higher L, andthen its intensity decreases, reaches a minimum, and increases as itslowly shifts back to lower L. The shifts in peak position map out thestrain changes of the chemical butterfly loop, while the minimum inintensity marks the point in the switching process when there are equalfractions of positive and negative domains. At t=12400 s, the atmosphereis changed back to the original high pO₂ environment. The sequence ofpeak position and intensity changes occurs again, although more rapidly,ending in a scattering pattern identical to the initial state.

FIG. 6B shows the distribution of scattering in the K (in-plane)direction as a function of time measured during the same switchingcycle. The appearance of in-plane diffuse scattering in concert with thereduction in intensity at K=0 is due to the mixed-domain state duringthe switching process. From the extent of the scattering in K, thetypical size of the domains at the midpoint of switching is determinedto be ˜20 nm. The switching of ferroelectric polarization indicates thatthe film surface strongly interacts with the surrounding chemicalenvironment. Significant surface charge density is required tocompensate the observed polarization of 0.6 C/m₂, which corresponds to0.6 electronic charges per unit cell area. Previous density functionaltheory (DFT) calculations (10) have shown that negative ion adsorbatessuch as O or OH could be responsible for compensating the surface ofpositively polarized films under high pO₂ conditions.

Without being bound by any theory of operation, we hypothesize that thespecies responsible for compensation of negatively polarized domainsunder low pO₂ conditions are positively charged surface point defectssuch as oxygen vacancies. The vacancy concentration on the surface couldbe 8 substantially larger than that which can be tolerated in the bulkand could provide sufficient charge compensation. In fact, we observethat a surface reconstruction with 4 1 symmetry forms under reducingenvironments. Its intensity scales closely with the fraction of negativedomains determined from the Bragg peak intensity, indicating that thisreconstruction is formed by an ordering of the positively chargedspecies compensating the surface of the negative domains.

Preliminary DFT calculations indicate that one oxygen vacancy per foursurface unit cells will stabilize negative polarization in an ultrathinPbTiO₃ film. We are still investigating the 4×1 reconstruction using insitu x-ray scattering, and the atomic scale structure remains to besolved. The pO₂ dependence of the lattice parameter of the monodomainstate is relatively weak at the extremes of pO₂ (regions I and III inFIG. 4), and becomes stronger at intermediate values (e.g. pO₂ between10⁻³ to 10⁻¹ mbar). We attribute this to a saturation in theconcentration of charged surface species at extremes of pO₂. In theintermediate region, the magnitude of the variation of c with log(pO₂)is about twice as large for positively polarized monodomain films thanfor negatively polarized films. Since the piezoelectric coefficients foropposite polarizations are expected to have equal magnitudes, this mayindicate a difference in the pO₂ dependence of the amount of surfacecharge. Chemical butterfly loops such as FIG. 4A thus provide directevidence for the nature of the charged species compensating the surface.The switching behavior observed in this study indicates that chemistryon the ferroelectric surface plays an important role in controlling thepolarization in ultrathin films without a top electrode. In particular,these results indicate that the chemical environment produces a surfacepotential that depends upon the composition of the ambient and is ingeneral non-zero; this should be taken into consideration when studyingsize effects on ferroelectricity. It is possible to use chemicalprocesses as a new method to create domain structures in ferroelectricfilms, including patterning through a lithographically produced mask.Conversely, the nature of ferroelectric film polarization can modifysurface chemical reactions. The ability to electrically switch thereactivity of a surface could form the basis for new classes ofthin-film chemical actuators and catalysts, offering dynamical controlof reactivity and selectivity over a wide range in a single system.Adsorption of both cations and anions on nanoscale 180° stripe domainswould provide a means for sub-lithographic-spatial-scale patternformation. Further understanding of the interactions of ambients withpolarization at ferroelectric surfaces promises to provide a new meansfor manipulating both ferroelectricity and surface chemistry.

Methods and Materials

The experiments were performed at beamline 12-ID-D of the AdvancedPhoton Source. The PbTiO₃ films were grown using metal-organic chemicalvapor deposition in a chamber designed for in-situ synchrotron x-raystudies of film growth and processing (S1). PbTiO₃ films were grown at930 K following procedures described previously (S2), using SrTiO₃ (001)substrates on which epitaxial SrRuO₃ films had been previously depositedby pulsed laser deposition in a separate chamber (S3). Both the SrRuO₃and PbTiO₃ layers were fully coherently strained to the SrTiO₃ in-planelattice parameter. Results presented were obtained from a sample having10 nm thick PbTiO₃ and 24 nm thick SrRuO₃ layers, as determined by x-rayscattering. Four additional samples having PbTiO₃ thicknesses of 6.4,10, 11, and 21 nm were found to have similar reversible switchingbehavior at various temperatures from 550 to 825 K. After growth, thesample was cooled in an oxidizing environment (pO₂=3.0 mbar) to thetemperatures for switching studies. The residual PbO vapor pressure inthe chamber was sufficient to maintain a PbO surface termination (S4).When changing the pO₂ of the gas mixture, the amount of N₂ carrier gaswas adjusted to keep the total active chamber flow at 1630 sccm.

The total chamber pressure was maintained at 13 mbar. Grazing incidencescattering of 28.3 keV x-rays was used for real-time monitoring of filmgrowth and film strain during changes in the vapor ambient. Theincidence angle was ≦1.0°, except for studies of the 4×1 reconstruction,where it was ≦0.11° (the critical angle). The x-ray scattering intensity(counts per second) shown in the plots has been normalized to correspondto a fixed incident flux typical of 100 mA current in the storage ring.

The chemical butterfly loops such as FIG. 4 were traced by changing pO₂in steps while performing repeated L scans through the PbTiO₃ 304 peakto monitor the strain changes. Dwell time at each intermediate pO₂ was800 s, equivalent to ˜10 scans. This was typically long enough for thelattice parameter to equilibrate, except in the switching regions.Values reported were obtained from the last scattering pattern recordedat a given pO₂ before the next step change. A longer dwell (e.g. 10,000s) was used to fully switch the sample at the extreme pO₂ conditionsbefore measuring the reverse half of the loop. Reciprocal spacecoordinates H, K, and L are given in reciprocal lattice units of theSrTiO₃ substrate at 298 K, which has a cubic lattice parameter of 3.9051Å (S5). To obtain accurate PbTiO₃ lattice parameter values from the 304peak position, the L offset was calibrated using the nearby Bragg peakfrom the SrTiO₃ substrate (using SrTiO₃ lattice parameters of 3.9194 Åand 3.9233 Å at 645 and 735 K, respectively (S5)). Evolution of thex-ray scattering distribution during switching, e.g. FIG. 7, was mappedby performing repeated scans alternating in the L and K directions whilea change was made between high and low pO₂ conditions. We found that theswitching behavior was reproducible and that equilibrated L scans wereidentical even after the sample had been removed from the chamber andexposed to air, as long as it was first heated to the growth temperature930 K with a PbO overpressure sufficient to maintain the PbO terminatedPbTiO₃ surface but below the value for PbO deposition (S4), and thencooled to lower temperatures in the same manner as done with theas-grown films.

To obtain the PbTiO₃ out-of-plane lattice parameter c and positivedomain fraction x_(pos) from the measured L scans, they were fit toscattering patterns calculated from an atomic-scale model of thePbTiO₃/SrRuO₃/SrTiO₃ film/substrate structure similar to that usedpreviously (S6). The model is based on the experimental determinationthat the films are coherently strained to the SrTiO₃ in-plane latticeconstant. The atomic structure of the SrTiO₃ and SrRuO₃ are modeled assimple perovskites, with centrosymmetric atomic positions. Deviations ofthe PbTiO₃ atomic positions from centrosymmetric sites are taken fromliterature values (S7) scaled linearly with polarization, where thepolarization is obtained from the lattice parameter using Landau theoryfor monodomain coherently-strained PbTiO₃ on SrTiO₃ (S8,S9). Thispredicts that the square of polarization, |P|², is a linear function ofthe out-of-plane strain, x₃, given by

$\begin{matrix}{{{P}^{2} = {\left( {Q_{11} - {\frac{2s_{12}}{s_{11} + s_{12}}Q_{12}}} \right)^{- 1}\left( {x_{3} - {\frac{2\; s_{12}}{s_{11} + s_{12}}x_{m}}} \right)}},} & ({S1})\end{matrix}$where Q₁₁, Q₁₂, s₁₁ and s₁₂ are the electrostrictive constants andelastic compliances of PbTiO₃, and x_(m) is the in-plane misfit strain.As is standard for this description, strains are defined with respect tothe state of zero polarization and zero stress, giving x₃≡(c−a₀)/a₀,x_(m)≡(a_(s)−a₀)/a₀, where c is the out-of-plane lattice parameter, a₀is the stress-free lattice parameter of the fictitious cubicparaelectric phase extrapolated to the temperature of interest, and_(s)a is the substrate lattice parameter. Values of these quantitiesobtained from measurements in the literature are summarized in reference(S8). The surface of the PbTiO₃ layer is assumed to be PbO terminated,consistent with the surface reconstructions found during the experiment.(We also fit the data to a TiO₂ terminated model, and found worseagreement.) Atomic displacements at the surface (e.g. due to surfacereconstructions) were not included in the model. The interface betweenthe SrRuO₃ and PbTiO₃ layers is assumed to have consecutive layers ofSrO and TiO₂. The lattice parameters of both films and substrate areassumed to be constants through the thickness, and the latticeparameters of oppositely polarized domains in the PbTiO₃ are assumed tobe the same. This is physically reasonable for domain fractions nearzero or unity, where the minority domains would tend to be strained tomatch the majority domains, but is not necessarily a good approximationfor domain fractions near 50%. Subsidiary structural parameters such asthe SrRuO₃ lattice parameter, the layer thicknesses, roughnesses ofinterfaces, and atomic-scale offsets between layers were determined byfitting extended scans through the PbTiO₃, SrRuO₃, and SrTiO₃ 304 peaksfrom L=3.6 to 4.1, recorded from the positively polarized monodomainsample at pO₂=3.0 mbar. The polarization direction of the high-pO₂monodomain state had been previously determined to be positive bypiezoforce microscopy (S6). Fits to our switching results, describedbelow, also give the same result. Figure S1 shows the fit for T=645 K.The summation of the scattering amplitudes from all layers produces thecomplex interference fringes.

To model the polydomain states during switching, two additionalstructural parameters had to be determined: the out-of-plane latticeoffset at 180° domain walls, and the fraction of the scattering fromoppositely polarized domains that sums incoherently, f_(inc). The domainwall offset was assumed to be proportional to polarization, with a valuechosen to reproduce the temperature dependence of the PbTiO₃ 304 peakintensity for samples with 180° stripe domains, which has a minimum at˜650 K (S10). The value of f_(inc) depends on the domain size relativeto the resolution of the scattering measurement.

For large domains or lower resolution, the scattering will addincoherently (f_(inc) approaches 1), while for small domains or higherresolution the scattering will add

coherently (f_(inc) approaches 0). The total intensity is given by1=f _(inc) [x _(pos) |F ₊|²+(1−x _(pos))|F ⁻|²]+(1−f _(inc))|x _(pos) F₊+(1−x _(pos))F ⁻|²where F₊ and F⁻ are the scattering amplitudes from the positively andnegatively polarized domains, respectively, including the contributionsfrom the substrate. FIG. 8 shows the intensity as a function of x_(pos)for three values of f_(inc). The minimum at x_(pos)=0.5 is due to thedestructive interference between the scattering from the oppositelypolarized domains. The minima in x-ray intensity we observe afterchanging pO₂ are thus signatures of domain switching. Such minima havebeen predicted theoretically (S11) and can also be seen in literaturedata taken during electrical switching experiments (e.g. see FIGS. 2 and3 of reference (S12)). Since the depth of the minimum depends onf_(inc), we choose its value to match the minimum intensity observedduring switching. Values of f_(inc) ranging from 0.1 to 0.5 were found,increasing for slower switching speeds, consistent with the effectexpected from larger domain sizes.

Using these parameters, fits were made to the short scans from L=3.75 to3.90 across the PbTiO₃ 304 peak obtained at various pO₂ conditionsduring measurements of the butterfly loops and switching dynamics. Theonly free parameters in these fits were the PbTiO₃ lattice constant xand the positive domain fraction x_(pos). By using Eq. (S1) relatinglattice parameter and polarization magnitude, the net polarization ofthe film |P|(1−2x_(pos)) can be calculated, as given in FIG. 4C. Theposition of the PbTiO₃ peak determines c (and thus |P|), and itsintensity determines x_(pos). The peak position and intensity for thedata of FIG. 6 are shown in FIG. 8. A comparison with the fit results inFIG. 7 illustrates the direct relationships. Since two values of x_(pos)can give the same intensity, there is some ambiguity in which solutionto choose, especially near x_(pos)=0.5. However, since the modelincludes anomalous scattering effects on atomic scattering factors, theintensity scattered from positively polarized PbTiO₃ is calculated to beabout 6% higher than that from negative at the x-ray energy used (28.3keV) (see FIG. 9). We observe a similar difference in the measurementsfor the extreme pO₂ cases, which provides further evidence that we areobserving switching and have correctly identified the polarizationdirections.

We observe weak effects of the incident x-ray intensity on the measuredstrain. The primary effect is that higher incident intensities increasethe speed with which the strain equilibrates when pO₂ is changed. Theincident intensity also has a small, reversible effect on theequilibrium strain values, with high intensities producing ˜0.1% largerstrains in both positively and negatively polarized films. These strainsare small compared with those measured due to pO₂ changes. The effectsare consistent with a hypothesis that reaction of molecular O₂ with thesurface is the rate-limiting step in the chemical switching process, andthat ionizing radiation increases the rate of this reaction (in both theoxidizing and reducing directions). Further studies of the reactionchemistry occurring at the surface are underway.

To address the question of whether surface oxygen vacancies canstabilize the negatively polarized domains at low pO₂, and the nature ofthe 4×1 reconstruction observed under these conditions, we performeddensity functional theory (DFT) calculations using methods describedpreviously (S6). The system size was 4 perovskite unit cells by 1 unitcell in plane, with a PbTiO₃ layer 2 unit cells thick on top of a SrRuO₃layer 3 unit cells thick, strained to an in-plane lattice parameterappropriate to match the experimental conditions. The surface andinterface terminations were the same as given above for the scatteringmodel. One oxygen vacancy was located in the surface PbO layer.

We found that the presence of the oxygen vacancy stabilized a negative(inward) polarization in the PbTiO₃ film. For this 2-unit-cell-thickfilm, the average polarization was only about 30% of that of bulk PbTiO₃at 0 K. We expect that the stabilization and polarization would increasefor thicker films, such as those studied experimentally. Table 2 gives acomparison of the ground state energy ΔE_(DFT) at T=0 K and theestimated enthalpy and free energies at T=735 K. These are differencesbetween the system with an oxygen vacancy plus a free oxygen atom,relative to the system with no oxygen vacancy (which we found to have anunpolarized ground state). As previously (S6), values are given pervapor atom, which in this case is per 4 perovskite surface unit cells.The free energy ΔG=ΔG°+kT ln pO has been calculated using an oxygenpartial pressure of pO₂=1×10⁻⁹ bar corresponding to typical experimentalconditions for the 4×1 reconstruction, which gives an oxygen atompressure at T=735 K of pO=9×10⁻²⁰ bar (S13). We expect the polar oxygenvacancy structure will become increasingly stable as the film thicknessincreases, by as much as −0.2 eV per added unit cell thickness (the DFTferroelectric well depth for bulk PbTiO₃ per four-unit-cell area). Basedon this estimate, PbTiO₃ films having a thickness of 4 unit cells orlarger would have a negative ΔG and this be favored over the unpolarizedsystem under the experimental T and pO₂ conditions.

TABLE 2 Calculated ground state (T = 0 K) energy ΔE_(DFT) andpolarization P/|P_(bulk)|, standard enthalpy ΔH° and free energy ΔG° atT = 735 K, and free energy ΔG at T = 735 K and pO = 9 10⁻²⁰ bar for atwo-unit-cell-thick PbTiO₃ layer containing one oxygen vacancy per fourunit cell surface area. ΔE_(DFT) ΔH° ΔG° ΔG Compensation P/|P_(bulk)|(eV) (eV) (eV) (eV) O vacancy (4 × 1) −0.3 4.36 4.42 3.05 0.27

REFERENCES METHODS AND MATERIALS

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What is claimed is:
 1. A method of reversibly switching the polarizationof a ferroelectric film, comprising: changing a chemical environment incontact with one surface of the ferroelectric film.
 2. The method ofclaim 1, wherein the chemical environment is changed by controlling theoxygen partial pressure in contact with the ferroelectric film.
 3. Themethod of claim 2, wherein the change in oxygen partial pressure inducesan outward or inward polarization, respectively, in the ferroelectricfilm.
 4. The method of claim 1, wherein the ferroelectric film comprisesa perovskite thin-film.
 5. The method of claim 4, wherein the perovskitethin-film comprises PbTiO₃.
 6. The method of claim 1 wherein theferroelectric film is supported on a conducting substrate.
 7. The methodof claim 1 wherein the ferroelectric film is thinner than 10 nm.